Finite Group Databasebeta

← C2×#20246316 #26375604

Subgroups — C2×#20246316 #26375604

Order 12032.

3894 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C22×#13093980C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246316C2116yesmaximal, direct product factor
5C2×#15689016C211yesmaximal, characteristic, complemented
6C2×#15689010C211yesmaximal, characteristic, complemented
7C2×#15689004C211yesmaximal, characteristic, complemented
8C2×#15688999C211yesmaximal, characteristic
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688987C211yesmaximal, characteristic, complemented
11C2×#15688982C211yesmaximal, characteristic, complemented
12C2×#15688981C211yesmaximal, characteristic, complemented
13C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×(C22⋊D47)⋊C4C4116yescomplemented
23C2×(C22⋊D47)⋊C4C2218yes—
24C2×#13093980—28no—
25C2×#13093980C2218yescomplemented
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C2×C4⋊C4×D47—28no—
33C2×C4⋊C4×D47C2218yescomplemented
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689016C2218yescomplemented
44#15689010C2218yescomplemented
45#15689004C2218yescomplemented
46#15688999C2218yes—
47#15688999C2218yes—
48#15688987C2218yescomplemented
49#15688982C2218yescomplemented
50#15688981C2218yescomplemented
51C4×Dic47⋊C4C2218yescomplemented
52C4×(C2×D47)⋊C4C2218yescomplemented
53#15688970C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47C2×C418yescomplemented
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47C2×C418yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98(C22⋊D47)⋊C4C2×C4164yescomplemented
99#13093980—232no—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47C2314yes—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4C2×C418yescomplemented
106C2×Dic47⋊C4D418yescomplemented
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C4⋊C4×D47—232no—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47—42no—
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4C2×C418yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47—42no—
126C2×C4×Dic47C2×C418yescomplemented
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—42no—
150C2×C22⋊C4×C47C2×C418yescomplemented
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—42no—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47#4114yes—
173C23×D47#4114yes—
174C23×D47C2412yes—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C2×D414yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—232no—
210C22×Dic47—28no—
211C22×Dic47—28no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47C22×C414yes—
222C22×Dic47C22×C414yes—
223C22×Dic47C22×C414yes—
224C22×Dic47C22×C4116yescomplemented
225C22×Dic47C2×D414yes—
226C22×Dic47C2×D414yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47—28no—
241C2×C4×D47—28no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—416no—
245C2×C4×D47—416no—
246C2×C4×D47C22×C4116yes—
247C4⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47—44no—
250C22⋊C4×C47C22×C4116yescomplemented
251C42×C47—44no—
252C22⋊Dic47—28no—
253C22⋊Dic47—44no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4C22×C4116yes—
257C4⋊Dic47—28no—
258Dic47⋊C4—28no—
259Dic47⋊C4—28no—
260Dic47⋊C4—28no—
261Dic47⋊C4C22×C4116yescomplemented
262Dic47⋊C4C2×D4116yescomplemented
263C4×Dic47—28no—
264C4×Dic47—28no—
265C4×Dic47—44no—
266C4×Dic47C22×C4116yescomplemented
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47H(5,𝔽2)12yes—
287C23×C472−1+412yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47#117116yescomplemented
300C22×D47C23×C414yes—
301C22×D47C2×#4114yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47—44no—
324C2×C4×C47C23×C414yes—
325C2×C4×C47C23×C414yes—
326C2×C4×C47C22×D414yes—
327C22⋊D47—232no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—232no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—44no—
348C2×Dic47—44no—
349C2×Dic47—44no—
350C2×Dic47C4×D4116yes—
351C2×Dic47C23×C414yes—
352C2×Dic47C23×C414yes—
353C2×Dic47C23×C414yes—
354C2×Dic47C22×D414yes—
355C2×Dic47C22×D414yes—
356C2×Dic47C2×#4114yes—
357C4×D47—232no—
358C4×D47—416no—
359C4×D47—416no—
360C2×#2352—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—416no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47C2×#11714yes—
370C22×C47C2×C4×D414yes—
371C22×C47#52014yes—
372C22×C47#54614yes—
373C22×C47#54814yes—
374C22×C47#55214yes—
375C22×C47#55314yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C2×H(5,𝔽2)11yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—232no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47C2×#11718yescomplemented
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47C2×C4×D418yes—
404C22×C4×D4—471no—
405C22×#117—471no—
406C23×C4⋊C4—471no—
407#2352—4716no—
408C2×#388—471no—
409C2×#388D4711yescharacteristic, complemented
410C2×#387—471no—
411C2×#387—471no—
412C2×#386—471no—
413C2×#386—471no—
414C2×#382—471no—
415C2×#380—471no—
416C2×#380—471no—
417C2×C4×C4⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C2×C4×C22⋊C4—471no—
420C2×C47—44no—
421C2×C47#235218yescomplemented
422C2×C47C22×#11711yescharacteristic
423C2×C47C22×C4×D411yescharacteristic
424C2×C47C2×#52011yescharacteristic
425C2×C47C2×#54611yescharacteristic
426C2×C47C2×#54811yescharacteristic
427C2×C47C2×#55211yescharacteristic
428C2×C47C2×#55311yescharacteristic
429D47—28no—
430C23×D4—471no—
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4—471no—
435C2×C4×D4—4716no—
436C2×C4×D4—478no—
437C2×#117—478no—
438C2×#117—948no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—478no—
446C22×C4⋊C4—948no—
447C22×C4⋊C4C2×D4711yescharacteristic
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4C2×D4711yescharacteristic
454C22×C22⋊C4C2×D4711yescharacteristic
455C22×C22⋊C4C2×D4711yescharacteristic
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42C2×D4711yescharacteristic
461#388—478no—
462#388C2×D4718yescomplemented
463#387—478no—
464#387—478no—
465#386—478no—
466#386—478no—
467#382—478no—
468#380—478no—
469#380—478no—
470C4×C4⋊C4—478no—
471C4×C22⋊C4—478no—
472C4×C22⋊C4—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×#235211yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—471no—
491C23×C4—478no—
492C23×C4—474no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—478no—
497C23×C4—474no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—471no—
501C23×C4—474no—
502C23×C4—474no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—944no—
511C23×C4—1882no—
512C23×C4—1882no—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519C4×D4—4764no—
520#117—9432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—478no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—9432no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4C22×D4714yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—478no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—474no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—944no—
545C2×C22⋊C4—944no—
546C2×C22⋊C4—944no—
547C2×C22⋊C4—1882no—
548C2×C22⋊C4C4×D4718yescomplemented
549C2×C22⋊C4C22×D4714yes—
550C2×C22⋊C4C22×D4714yes—
551C2×C22⋊C4C22×D4714yes—
552C2×C42—42no—
553C2×C42—478no—
554C2×C42—474no—
555C2×C42—474no—
556C2×C42—474no—
557C2×C42—474no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42—1882no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—9432no—
591C2×D4—948no—
592C2×D4—948no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—474no—
611C22×C4—472no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—4716no—
615C22×C4—474no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—4716no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—948no—
624C22×C4—9432no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—948no—
629C22×C4—948no—
630C22×C4—9432no—
631C22×C4—948no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—948no—
648C22×C4—1884no—
649C22×C4—1884no—
650C22×C4—18816no—
651C22×C4—18816no—
652C22×C4C2×C4×D4714yes—
653C22×C4C2×C4×D4714yes—
654C22×C4D4×D4714yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—28no—
662C4⋊C4—4716no—
663C4⋊C4—4716no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—948no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—4716no—
671C22⋊C4—948no—
672C22⋊C4—948no—
673C22⋊C4—948no—
674C22⋊C4—1884no—
675C22⋊C4C2×C4×D47116yescomplemented
676C42—44no—
677C42—4716no—
678C42—948no—
679C42—948no—
680C42—1884no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—948no—
703C23—948no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#41×D4712yes—
713C23#41×D4712yes—
714C23#1309406912yes—
715C23#1309407112yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—4716no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—474no—
745C2×C4—474no—
746C2×C4—9432no—
747C2×C4—9432no—
748C2×C4—948no—
749C2×C4—948no—
750C2×C4—948no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—18816no—
767C2×C4—18816no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4—1884no—
771C2×C4C22×C4×D4714yes—
772C2×C4C22×C4×D4714yes—
773C2×C4C2×D4×D4714yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—478no—
783C22—944no—
784C22—9432no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22—944no—
789C22—944no—
790C22#117×D4714yes—
791C22C4×D4×D4714yes—
792C22#1568960214yes—
793C22#1568976214yes—
794C22#1568978114yes—
795C22#1568980914yes—
796C22#1568981814yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C2×#41×D4711yescharacteristic
802C22C2×#1309406911yescharacteristic
803C22C2×#1309407111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—478no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—948no—
819C2#2024631618yesdirect product factor
820C2C2×#117×D4711yescharacteristic
821C2C2×C4×D4×D4711yescharacteristic
822C2C2×#1568960211yescharacteristic
823C2C2×#1568976211yescharacteristic
824C2C2×#1568978111yescharacteristic
825C2C2×#1568980911yescharacteristic
826C2C2×#1568981811yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2352
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#13093980C2semidirect
3. C22×C4⋊C4×D47C2semidirect
4. #20246316C2direct (N × H)
5. C2×#15689016C2semidirect
6. C2×#15689010C2semidirect
7. C2×#15689004C2semidirect
10. C2×#15688987C2semidirect
11. C2×#15688982C2semidirect
12. C2×#15688981C2semidirect
13. C2×C4×Dic47⋊C4C2semidirect
14. C2×C4×(C2×D47)⋊C4C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
22. C2×(C22⋊D47)⋊C4C4semidirect
25. C2×#13093980C22semidirect
33. C2×C4⋊C4×D47C22semidirect
43. #15689016C22semidirect
44. #15689010C22semidirect
45. #15689004C22semidirect
48. #15688987C22semidirect
49. #15688982C22semidirect
50. #15688981C22semidirect
51. C4×Dic47⋊C4C22semidirect
52. C4×(C2×D47)⋊C4C22semidirect
53. #15688970C22semidirect
67. C47×#388C22semidirect
77. C23×Dic47C2×C4semidirect
98. (C22⋊D47)⋊C4C2×C4semidirect
105. C2×Dic47⋊C4C2×C4semidirect
106. C2×Dic47⋊C4D4semidirect
126. C2×C4×Dic47C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
224. C22×Dic47C22×C4semidirect
250. C22⋊C4×C47C22×C4semidirect
261. Dic47⋊C4C22×C4semidirect
262. Dic47⋊C4C2×D4semidirect
266. C4×Dic47C22×C4semidirect
299. C22×D47#117semidirect
390. C2×D47C2×#117semidirect
409. C2×#388D47semidirect
421. C2×C47#2352semidirect
462. #388C2×D47semidirect
483. C47C2×#2352semidirect
548. C2×C22⋊C4C4×D47semidirect
675. C22⋊C4C2×C4×D47semidirect
819. C2#20246316direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×(C22⋊D47)⋊C42
C22×#130939802
C22×C4⋊C4×D472
#202463162
C2×#156890162
C2×#156890102
C2×#156890042
C2×#156889992
C2×#156889872
C2×#156889822
C2×#156889812
C2×C4×Dic47⋊C42
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×C47×#3882
C2×#235247